Litter boxes filled with litter material are commonly used for domestic animals such as cats and dogs as convenient means of containment for urine and excrement. Such boxes are generally rectangular in shape having the dimensions of, for example, approximately 50 centimeters in length by 36 centimeters in width, with vertical side walls of, for example, approximately 10 centimeters in height. Such boxes are filled to a depth of approximately 5 to 10 centimeters with granular litter material which absorbs urine and deodorizes. The litter material is customarily left in the litter box for a period of 7 to 10 days after which it is disposed of and replaced. During such period, however, solid waste must be separated from the litter material for disposal. The removal of solid waste from the litter material requires the use of a scooping tool or glove and is generally a messy and unsanitary process. Aversion to the undesirable task of removing solid waste from the litter box often prompts disposal of all of the litter material prior to expiration of its useful life. As urine is absorbed by the litter material, dampened spots develop clumps in uncirculated litter which, if not dispersed or removed, concentrate odor production and shorten the useful life of the litter material. Also, direct contact of the litter material and animal waste with the interior of the litter box results in soiling and contamination of the box, necessitating cleaning of the box with each changing of the litter material.